Short Time Furrier Transform is difference FFT

furrier transform

hi
Short Time Furrier Transform is difference FFT.
How to use for applications
thank

fft real signal

yep. in short time fourier you will get the resolution in time too. if you use fft, u will neverknow when you signal happen. It is called time-frequency analysis. Spectrogram is a good example.

when not to use fft

Hi,

Discrete Fourier Transform (DFT) transforms discrete time domain into complex (Real and Imaginary) discrete frequency domain and assumes the origin of time in -infinity and the end of time in + infinity.

So if you want to apply DFT (implemented with some efficient FFT algorithm) on real noisy signals with finite duration you need to use some window function or short time-Fourier transform.

For example if you want to determine frequency of noisy radar impulse you need to use windowing or some other 3D-spectrum analysis estimation method like periodogram with overlapping or filter bank.

For additional explanations take some good DSP classic book.

Regards

fft of diff signal

Just thought Id add, that if you want a space to frequency alg thats easier to use, takes less computer time but only deals with real data (no i componants) then try looking up the Hartley transform.

fast fourier transform dif

I think window function is not a short-time fouier transform. the window is used since you real world signal have a finite duration so you trancate the infinite sesquence with a window. of u dont use window function, u will get a rectangular pulse modulate aith your signal it shows up as a many ripple in frequency domain because the pulse function is a sinc function in frequency domain. you use a window function to get rid of those ripple. THe shor-time fourier transform is different. It is a tool to do time-frequency analysis. You should take a look at the book in time-freqncy analysis like a book by Cohen, time-frequency analysis.

stft dct wavelet

Hi,

Of course that short-time Fourier transform is not window function. You cannot apply DFT transform on short-time signal so one of solutions is to use short-time Fourier transform.

But you can use DFT with appropriate window function to estimate some parameters from signal. Also you can use and many other transforms for this purpose e.g Walsh, DCT or optimal (but unefficent) KL tranform.

Usign some transform you tranform time domain in some other domain which is suitable for data analysis or for data compresion.

Fourier transorm has strong physical mean because you can easy determine harmonics from time signal and e.g true effective value or harmonic distortion.

DCT compresses information in small number of coefficients and it is useful for compression of real images.

Regards

difference in stft and fft

Even a long-time signal u can use short-time fourier transform why not? spectrogram for speech signal is a good example.

short time fourier transform overlap

Short-time fourier transsform is a analysis tool. The result may not be used to resconstruct the signal. Your time-frequency frame (sometime it is called Garber Frame) have to satisfy unertianty princitple. While DCT, wavelet, KLT is a signal approximation. You can also use it to analize signal also but your transformed signal has not much meaning in physic. IN the case of signal compression, who care? we just need the one that give the lowest entropy. But in signal analysis, it is crucial. how to reconstruct the signal is not importance. Fourier transform is not so good in signal compression since it may map from real/integer to complex numer so u have twice as much as data. To get a real specrum, you need a self-adjoint operator which DCT is one of them. That why they use DCT for image but DCT has it own problem. The image is an integer. if we map from interger to real, your entropy increase. Hence we need a quantizer. Wavelet is much better, besides it is a self adjoint operator, it have a property such as vanishing moment, so you can deaign you wavelet so that you series is not too long since after a certain value, all coefficients will be zero. There is also an implaementation of the wavelet transform that can map from interger to integer (lifting scheme) so you dont loss any information in quantizattion process. KLT is optimal since it use the signal itself to construct the basis; hence you get the real signal space from the undelying signal. It is not so efficient since you have to compute the basis everytimg u need to do a transformation.

furrier analysis

About STFT look here:
https://www.math.ucdavis.edu/~strohmer/research/gabor/gaborintro/node3.html

It is possible to reconstruct the original time Signal from the Short time fourier transformed values. It is neccessary to convert overlaping time segments to freqeuncy domain and back. The in time domain the have to be overlap added.

STFT is not so efficient like FFT when transforming and representing time signals. But the time resolution for each STFT block is much better than in FFT.

stft unterschied fft

Maybe I have it wrong, but my understanding is that, from the point of view of operations performed, the STFT and FFT are exactly the same. The only difference is that in the STFT case, you will apply FFT (and any windowing you might find usefull for your application) on a bunch of sub-sequences of the original sequence, whereas in the non-short-time application you will try to apply the FFT to the entire signal that is being analyzed.

Am I incorrect ?